Following [1]}, the work of Censor-Hillel, Le Gall, and Leitersdorf [2]} provided algorithms for listing \(p\) -cliques in \(\tilde{O}(n^{p/(p+2)})\)  rounds, w.h.p., for all \(p\ge 4\)  except for \(p=5\) . For \(p=5\) , this work gave an algorithm which completes in \(\tilde{O}(n^{3/4+o(1)})\)  rounds, w.h.p. The main approach of these algorithms is iterating over the decomposition in a way that balances the minimum degree and the arboricity thresholds. Within each cluster, sparsity-aware listing helps speeding up the computation. While these algorithms improved upon the state-of-the-art for \(p=4,5\)  and were the first sublinear algorithms for \(p\ge 6\) , they fell short of the [3]} lower bound of \(\tilde{\Omega }(n^{1-2/p})\)  rounds. The question of whether clique listing in the \(\mathsf {CONGEST}\)  model is as easy as, or harder than, its \(\mathsf {CLIQUE}\)  counterpart, was recently answered by Censor-Hillel, Chang, Le Gall, and Leitersdorf [4]}, using the newer conductance decomposition of Chang and Saranurak [5]} and additional mechanisms for optimal sparsity-aware listing and for efficient transmission of edges in the clutsers.
